by Richard M. Scheffler and Daniel R. Arnold

The reported 22 percent average increase in its premiums last year was perhaps the sharpest dagger plunged into the Affordable Care Act. But a better measure that reflects what enrollees actually paid tells a very different story. Indeed, using that measure, it would seem that the California Affordable Care Act marketplace — known as Covered California — is a success that President-elect Donald Trump should look at closely to model.

Health insurance in the Affordable Care Act is sold in markets operated either at the state level, as in California, or through the federal exchange healthcare.gov. The basic idea is: Competition among insurers, driven by consumers shopping among plans, would lower price and improve value. The California exchange was set up to make plan comparison and shopping as easy as possible. All plans within a coverage tier have the same benefits and co-payments for each insurance product.

Shopping on the exchange is like shopping for most other things — the average purchase price depends on how many of each tier of policies are purchased, not the average of the prices asked.

Suppose we want to buy a car and there are only three types available: a $35,000 Toyota Prius, a $65,000 BMW, and a $90,000 Jaguar. The average offer price of these cars is $63,333, but suppose 60 percent of individuals purchase a Toyota Prius, 30 percent purchase a BMW, and 10 percent a Jaguar. Because of consumer shopping, the average purchase price of a car ends up being $49,500, or 22 percent below the average offer price.

Our new Health Affairs study shows that the Covered California insurance purchase price in 2016 was 15.2 percent less than the average offered price ($312 a month versus $368).

With subsidies based on income and age (89 percent of enrollees are subsidy eligible), the actual average premium paid by enrollees in California was only $156 a month.

Our study also found that a $100 annual increase in premiums (about $8 a month) would lead to a significant decrease in the probability a shopper would buy the plan. Not surprisingly, small changes in premium costs can lead to a great deal of switching. And we note: This is what is supposed to happen in a well-functioning market.

So what is the true story line with the Affordable Care Act exchanges and premium increases? The exchange in California was highly effective and had all the ingredients necessary for competition among insurers. Here, the markets worked just as intended.

True, switching plans may have caused problems for enrollees who also had to switch doctors and hospitals. However, these enrollees made this trade-off in exchange for lower premiums.

Consequently, the actual increase in insurance premiums paid in the state was about half. Premium costs offered rose 5.4 percent compared with 2.7 percent for premiums actually purchased. By this measure, the Affordable Care Act marketplace in California could be considered a huge success.

It is very likely that similar stories played out in other states across the country, but data is only publicly available in California. The Affordable Care Act isn’t broken — at least in California.

The Affordable Care Act’s potential successor is likely to do away with income-related insurance subsidies and taxes on high-income individuals and insurers. Without these subsidies, the cost of insurance for low-income individuals will be prohibitive and the rate of Americans without health insurance will balloon. Trump and his team certainly know this, as do the Democrats.

So what might the replacement look like?

From what we know so far, some of the likely components would include selling health insurance across state lines to encourage competition among insurers; giving flat tax credits, rather than giving tax credits based on income, for the purchase of insurance; and creating medical savings accounts to allow individuals to put tax-free income into an account that can be used to pay future health care expenses.

The simple truth is that health care is very expensive and the cost is likely to continue to increase. If access to health insurance that covers a basic benefit package of needed services is to be affordable for low- and middle-income families, then government subsidies will be required.

The only remaining question is who will pick up the bill and how. Truth be told, after shopping, we bought two Toyota Priuses.

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Richard M. Scheffler is a professor of health economics and public policy at the School of Public Health and the Goldman School of Public Policy at UC Berkeley. Daniel R. Arnold is a researcher at the UC Berkeley School of Public Health.